{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Kalman Filter for Sensor Fusion"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Idea Of ​​The Kalman Filter In A Single-Dimension\n",
    "\n",
    "Kalman filters are discrete systems that allows us to define a dependent variable by an independent variable, where by we will solve for the independent variable so that when we are given measurements (the dependent variable),we can infer an estimate     of the independent variable assuming that noise exists from our input measurement and noise also exists in how we’ve modeled the world with our math equations because of inevitably unaccounted for factors in the non-sterile world.Input variables become more valuable when modeled as a system of equations,ora  matrix, in order to make it possible to determine the relationships between those values. Every variables in every dimension will contain noise, and therefore the introduction of related inputs will allow weighted averaging to take place based on the predicted differential at the next step, the noise unaccounted for in the system,and the noise introduced by the sensor inputs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 294,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.mlab as mlab\n",
    "import seaborn as sb\n",
    "from scipy import stats\n",
    "import time\n",
    "from numpy.linalg import inv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 295,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "fw = 10 # figure width"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##  *Despite noisy measurement of individual sensors, We can calculate an optimal estimate of all conditions*."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### https://in.udacity.com/course/artificial-intelligence-for-robotics--cs373"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Plot the Distributions in this range:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 296,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = np.linspace(-100,100,1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 297,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "mean0 = 0.0   # e.g. meters or miles\n",
    "var0  = 20.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 298,
   "metadata": {},
   "outputs": [
    {
     "data": {
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gZ9KdliRJaq2aEq4mAo8BxBinA2MbtQ0HFscYq2OMe4CpwBkNbd8HfgasTq67kiRJrdsR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\n+QYHbO8YY10I4f+RCVo5wA0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      "text/plain": [
       "<matplotlib.figure.Figure at 0x271d960ad30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(fw,5))\n",
    "plt.plot(x,mlab.normpdf(x, mean0, var0), label='Normal Distribution')\n",
    "plt.ylim(0, 0.1);\n",
    "plt.legend(loc='best');\n",
    "plt.xlabel('Position');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Now we have something, which estimates the moved distance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### The Mean is  meters, calculated from velocity*dt or step counter or wheel encoder ...\n",
    "\n",
    "#### VarMove is the Estimated or determined with static measurements"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 299,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "meanMove = 25.0\n",
    "varMove  = 10.0 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 300,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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8DFeStI/S6TT3TM0Egw9PODzH1bQ+oX85QweUM2fhOuYvc+yV2h7DlSTtozmL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\nJClB/x+YhW8QKsekkQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x271d96c4ba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(fw,5))\n",
    "plt.plot(x,mlab.normpdf(x, meanMove, varMove), label='Normal Distribution')\n",
    "plt.ylim(0, 0.1);\n",
    "plt.legend(loc='best');\n",
    "plt.xlabel('Distance moved');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Both Distributions have to be merged together\n",
    "$\\mu_\\text{new}=\\mu_\\text{0}+\\mu_\\text{move}$ is the new mean and $\\sigma^2_\\text{new}=\\sigma^2_\\text{0}+\\sigma^2_\\text{move}$ is the new variance.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 301,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def predict(var, mean, varMove, meanMove):\n",
    "    new_var = var + varMove\n",
    "    new_mean= mean+ meanMove\n",
    "    return new_var, new_mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 302,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "new_var, new_mean = predict(var0, mean0, varMove, meanMove)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 303,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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sOGT5++9PZc2avyrs73C++OITABYunM/XX39Z7f1qk24iKiIi9VKvXr155JEn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\n/wG6os6e8hsWfgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x271d974a0f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(fw,5))\n",
    "plt.plot(x,mlab.normpdf(x, mean0, var0), label='Beginning Normal Distribution')\n",
    "plt.plot(x,mlab.normpdf(x, meanMove, varMove), label='Movement Normal Distribution')\n",
    "plt.plot(x,mlab.normpdf(x, new_mean, new_var), label='Resulting Normal Distribution')\n",
    "plt.ylim(0, 0.1);\n",
    "plt.legend(loc='best');\n",
    "plt.title('Normal Distributions of 1st Kalman Filter Prediction Step');\n",
    "plt.savefig('Kalman-Filter-1D-Step.png', dpi=150)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### What you see: The resulting distribution is flat > uncertain.\n",
    "\n",
    "The more often you run the predict step, the flatter the distribution get\n",
    "\n",
    "First Sensor Measurement (Position) is coming in...\n",
    "#### Sensor Defaults for Position Measurements\n",
    "(Estimated or determined with static measurements)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 304,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "meanSensor = 25.0\n",
    "varSensor  = 12.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 305,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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7D0qdYLiSpJRtqN3Bvc+sZFB5KVf1gNOBextTXc5Fp4xjy7Zd3OXs7VKHDFeSlKJcLsev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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x271d90aba90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(fw,5))\n",
    "plt.plot(x,mlab.normpdf(x, meanSensor, varSensor))\n",
    "plt.ylim(0, 0.1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now both Distributions have to be merged together\n",
    "$\\sigma^2_\\text{new}=\\cfrac{1}{\\cfrac{1}{\\sigma^2_\\text{old}}+\\cfrac{1}{\\sigma^2_\\text{Sensor}}}$ is the new variance and the new mean value is $\\mu_\\text{new}=\\cfrac{\\sigma^2_\\text{Sensor} \\cdot \\mu_\\text{old} + \\sigma^2_\\text{old} \\cdot \\mu_\\text{Sensor}}{\\sigma^2_\\text{old}+\\sigma^2_\\text{Sensor}}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 306,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def correct(var, mean, varSensor, meanSensor):\n",
    "    new_mean=(varSensor*mean + var*meanSensor) / (var+varSensor)\n",
    "    new_var = 1/(1/var +1/varSensor)\n",
    "    return new_var, new_mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 307,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "var, mean = correct(new_var, new_mean, varSensor, meanSensor)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 308,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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RAFK4EhEREQkghSsRESmTFi78i169urN7967sZa+//kr2Y2JOxMSJb9K375UM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\njj+c+wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x271d89dbf28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(fw,5))\n",
    "plt.plot(x,mlab.normpdf(x, new_mean, new_var), label='Beginning (after Predict)')\n",
    "plt.plot(x,mlab.normpdf(x, meanSensor, varSensor), label='Position Sensor Normal Distribution')\n",
    "plt.plot(x,mlab.normpdf(x, mean, var), label='New Position Normal Distribution')\n",
    "plt.ylim(0, 0.1);\n",
    "plt.legend(loc='best');\n",
    "plt.title('Normal Distributions of 1st Kalman Filter Update Step');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### This is called the Measurement or Correction step! The Filter get's more serious about the actual state."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Let's put everything together: The 1D Kalman Filter\n",
    "\"Kalman-Filter: Predicting the Future since 1960\"\n",
    "\n",
    "Let's say, we have some measurements for position and for distance traveled. Both have to be fused with the 1D-Kalman Filter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 309,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "positions = (10, 20, 30, 40, 50)+np.random.randn(5)\n",
    "distances = (10, 10, 10, 10, 10)+np.random.randn(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 310,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 10.80787218,  19.82024685,  30.24995934,  40.83244351,  49.49697058])"
      ]
     },
     "execution_count": 310,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "positions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 311,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  9.27854437,  10.25773141,   7.81942752,   8.19073928,   8.61443343])"
      ]
     },
     "execution_count": 311,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "distances"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 312,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "After correction:  mean= 20.02\tvar= 7.29\n",
      "After correction:  mean= 24.10\tvar= 7.08\n",
      "After correction:  mean= 30.94\tvar= 7.05\n",
      "After correction:  mean= 40.13\tvar= 7.04\n",
      "After correction:  mean= 49.19\tvar= 7.04\n"
     ]
    },
    {
     "data": {
      "image/png": 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EerriqnRsQAXo7mOeNRwvqhsGyinPpai6mG5+0TgpHNNWAejZwXyK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\ndyz5NU4Eudl+K5fJZASFeJF+PJ/iwkr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841PEYjHy8vL5xje+iU6n46677ubee+9GECSU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3xXtIpoLBfnB0d+wt5xaxrlsrI27l1xO02uFpxXML4ycDzCtpd7iEUyOGRo8qaoT3fjMfqQaxTk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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x271d72da5c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for m in range(len(positions)):\n",
    "    \n",
    "    # Predict\n",
    "    var, mean = predict(var, mean, varMove, distances[m])\n",
    "    #print('mean: %.2f\\tvar:%.2f' % (mean, var))\n",
    "    plt.plot(x,mlab.normpdf(x, mean, var), label='%i. step (Prediction)' % (m+1))\n",
    "    \n",
    "    # Correct\n",
    "    var, mean = correct(var, mean, varSensor, positions[m])\n",
    "    print('After correction:  mean= %.2f\\tvar= %.2f' % (mean, var))\n",
    "    plt.plot(x,mlab.normpdf(x, mean, var), label='%i. step (Correction)' % (m+1))\n",
    "    \n",
    "plt.ylim(0, 0.1);\n",
    "plt.xlim(-20, 120)\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "The sensors are represented as normal distributions with their parameters ($\\mu$ and $\\sigma^2$) and are calculated together with addition or convolution. The prediction decreases the certainty about the state, the correction increases the certainty.\n",
    "\n",
    "Prediction: Certainty $\\downarrow$\n",
    "Correction: Certainty $\\uparrow$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Kalman Filter - Multi-Dimensional Measurement"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Multidimensional Kalman filter\n",
    "\n",
    "\n",
    "Let's assume we drive our car  into a tunnel. The GPS signal is gone. Nevertheless, we might want to get notified that should  exit in the tunnel.The procedure is using the example of a vehicle with navigation device, which enters a tunnel. The last known position is before losing the GPS signal. Afterwards (with permanently installed Navis) only the speed information of the vehicle (wheel speeds & yaw rate) is available as normal distributed noisy measured variable. From this a velocity in x and y can be calculated. \n",
    "\n",
    "#### *How would we know now where we are right now? \n",
    "\n",
    "##### *It merges the vehicle sensors and calculates the position as well as possible.*\n",
    "\n",
    "\n",
    "\n",
    "Now lets think, when we were at the tunnel entrance last and drive at 50km / h, then the car can indeed calculated exactly where (x = position) you are 1 minute (t = time) later\n",
    "\n",
    "\n",
    "So far the perfect world. But the calculation takes over a microcontroller and this relies on sensors. Both the sensors have random errors, the transmission path has interference, and the resolution of CAN bus or analog-to-digital converters can cause many inaccuracies in the simple statement \"speed\". For example, a speed signal looks like this:\n",
    "\n",
    "Speed-time course of a measurement\n",
    "Speed-time course of a measurement\n",
    "\n",
    "On average, the measured speed is already correct, but there is some \"noise\". If one calculates a histogram of the determined speeds, one sees that the determined values ​​are approximately subject to a normal distribution.\n",
    "\n",
    "Histogram of measured velocity with normal distribution\n",
    "Histogram of measured velocity with normal distribution\n",
    "\n",
    "So there is one, and really only one, maximum value (unimodal) and a spread (variance). If this is the case, you can do the calculation very well with a trick nevertheless.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "### State Vector\n",
    "Constant Velocity Model for Ego Motion\n",
    "\n",
    "$$x_k= \\left[ \\matrix{ x \\\\ \\dot x \\\\ } \\right] = \\matrix{ \\text{Position X}  \\\\ \\text{Velocity in X} \\\\ }$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 313,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.]\n",
      " [ 0.]] (2, 1)\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.stats import norm\n",
    "\n",
    "x = np.matrix([[0.0, 0.0]]).T\n",
    "print(x, x.shape)\n",
    "#plt.scatter(float(x[0]),float(x[1]), s=100)\n",
    "#plt.title('Initial Location')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 314,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[100   0]\n",
      " [  0   9]] (2, 2)\n"
     ]
    }
   ],
   "source": [
    "P = np.diag([100, 9])\n",
    "print(P, P.shape)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Using Matplotlib to understand the P matrix More:\n",
    "\n",
    "The value of the vectors on the x,y and $\\dot x$, $\\dot y$ is very high. Thus the intial position and velocity is very uncertain\n",
    "\n",
    "While plotting the matrix, make sure we label:\n",
    "1. Setting the locations of the yticks\n",
    "2. Setting the locations and labels of the yticks\n",
    "3. Setting the locations of the yticks\n",
    "4. Setting the locations and labels of the yticks\n",
    "\n",
    "\n",
    "## Covariance matrix $P$\n",
    "\n",
    "An uncertainty must be given for the initial state  x0 . In the 1D case, the σ0 , now a matrix, defines an initial uncertainty for all states.\n",
    "\n",
    "This matrix is ​​most likely to be changed during the filter passes. It is changed in both the Predict and Correct steps. If one is quite sure about the states at the beginning, one can use low values ​​here, if one does not know exactly how the values ​​of the state vector are, the covariance matrix should be Pinitialized with very large values ​​(1 million or so) to allow the filter to converge relatively quickly (find the right values ​​based on the measurements).\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 315,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x271d9120e48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(6, 6))\n",
    "im = plt.imshow(P, interpolation=\"none\", cmap=plt.get_cmap('binary'))\n",
    "plt.title('Initial Covariance Matrix $P$')\n",
    "ylocs, ylabels = plt.yticks()\n",
    "plt.yticks(np.arange(7))\n",
    "# \n",
    "plt.yticks(np.arange(6),('$x$', '$y$', '$\\dot x$', '$\\dot y$'), fontsize=22)\n",
    "xlocs, xlabels = plt.xticks()\n",
    "# \n",
    "plt.xticks(np.arange(7))\n",
    "\n",
    "plt.xticks(np.arange(6),('$x$', '$y$', '$\\dot x$', '$\\dot y$'), fontsize=22)\n",
    "\n",
    "plt.xlim([-0.5,3.5])\n",
    "plt.ylim([3.5, -0.5])\n",
    "\n",
    "from mpl_toolkits.axes_grid1 import make_axes_locatable\n",
    "divider = make_axes_locatable(plt.gca())\n",
    "cax = divider.append_axes(\"right\", \"5%\", pad=\"3%\")\n",
    "plt.colorbar(im, cax=cax);\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Dynamics matrix A\n",
    "The core of the filter, however, is the following definition, which we would set up yourself only with great understanding of the physical context. This is not easy for many real problems. For our simple example (in-plane motion), the physics behind it comes from the smooth motion. The position results in xt + 1= x˙t⋅ t + xt and in velocity x˙t + 1= x˙t . For the state vector shown above, the dynamics in matrix notation is as follows:\n",
    "\n",
    "\n",
    "This states \"where\" the state vector moves from one calculation step to the next within dt . This dynamic model is also called a \"constant velocity\" model because it assumes that the velocity remains constant during a filter's calculation step.\n",
    "\n",
    "\n",
    "As an example, only the first line is written out, which calculates the position after a calculation step with the duration dt .\n",
    "\n",
    "## *xt + 1= xt+ dt ⋅ x˙t*\n",
    "This simply reflects physical relationships for the uniform motion. A higher form would be the Constant Acceleration model, which would be a 6D filter and still includes the accelerations in the state vector. In principle, other dynamics can be specified here (eg a  holonomic vehicle )."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Initial conditions / initialization\n",
    "System state x\n",
    "At the beginning you have to initialize with an initial state. In the 1 Dimensional case, μ0 , now in the multidimensional, was a vector.\n",
    "\n",
    "If nothing is known, you can simply enter 0 here. If some boundary conditions are already known, they can be communicated to the filter. The choice of the following covariance matrix P controls how fast the filter converges to the correct (measured) values."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " ### Time Step between Filter Steps $dt$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 316,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "dt = 0.1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Measurement Matrix $H$\n",
    "\n",
    "\n",
    "The filter must also be told what is measured and how it relates to the state vector. In the example of the vehicle, what enters a tunnel, only the speed, not the position! The values ​​can be measured directly with the factor 1 (ie the velocity is measured directly in the correct unit), which is why in only 1.0 is set to the appropriate position.H"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 317,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.   0.1]\n",
      " [ 0.   1. ]] (2, 2)\n",
      "[[ 0.05]\n",
      " [ 0.1 ]] (2, 1)\n",
      "[[ 1.  0.]\n",
      " [ 0.  1.]] (2, 2)\n"
     ]
    }
   ],
   "source": [
    "A = np.matrix([[1, dt],[0,1]])\n",
    "print(A, A.shape)\n",
    "\n",
    "\n",
    "\n",
    "B = np.matrix([[0.5*dt],[dt]])\n",
    "print(B, B.shape)\n",
    "\n",
    "\n",
    "H = np.matrix([[1.0, 0.0],\n",
    "              [0.0,  1.0]])\n",
    "print(H, H.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Measurement Noise Covariance $R$\n",
    "\n",
    "Measurement noise covariance matrix R\n",
    "As in the one-dimensional case the variance , a measurement uncertainty must also be stated here.σ0\n",
    "\n",
    "\n",
    "This measurement uncertainty indicates how much one trusts the measured values ​​of the sensors. Since we measure only $\\dot x$ and  $\\dot y$ , this is a 2 × 2 matrix. If the sensor is very accurate, small values ​​should be used here. If the sensor is relatively inaccurate, large values ​​should be used here for  $\\dot x$, $\\dot y$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 318,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 100.    0.]\n",
      " [   0.  100.]] (2, 2)\n"
     ]
    }
   ],
   "source": [
    "ra = 10.0**2\n",
    "\n",
    "R = np.matrix([[ra, 0.0],\n",
    "              [0.0, ra]])\n",
    "print(R, R.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Plot between -10 and 10 with .001 steps."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 319,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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JoktqoBymb2ic0x1DyIplZGeld/WISOTnZLJueREnmgcYHEkOz0+JP+EfXQ3v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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x271d85680f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xpdf = np.arange(-10, 10, 0.001)\n",
    "plt.subplot(121)\n",
    "plt.plot(xpdf, norm.pdf(xpdf,0,R[0,0]))\n",
    "plt.title('$\\dot x$')\n",
    "\n",
    "plt.subplot(122)\n",
    "plt.plot(xpdf, norm.pdf(xpdf,0,R[1,1]))\n",
    "plt.title('$\\dot y$')\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 320,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(2, 2)\n"
     ]
    }
   ],
   "source": [
    "sv = 8.8\n",
    "\n",
    "#G = np.matrix([[0.5*dt**2],\n",
    "#              [0.5*dt**2],\n",
    "#               [dt],\n",
    "#               [dt]])\n",
    "\n",
    "#Q = G*G.T*sv**2\n",
    "Q = np.matrix([[1, 0],[0, 1]])\n",
    "print(Q.shape)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 321,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[1, 0],\n",
       "        [0, 1]])"
      ]
     },
     "execution_count": 321,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Unit matrix $I$\n",
    "Last but not least a unit matrix is ​​necessary."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 322,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.  0.]\n",
      " [ 0.  1.]] (2, 2)\n"
     ]
    }
   ],
   "source": [
    "I = np.eye(2)\n",
    "print(I, I.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Measurements"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 323,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(200, 1) u\n",
      "(200, 1)\n",
      "Standard Deviation of Acceleration Measurements=1.93\n",
      "You assumed 100.00 in R.\n"
     ]
    },
    {
     "data": {
      "image/png": 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Rs/PSxRVHlN2wg6O9jMVo4+9adRJShDo2LsueqtrEcu3lMbMcTRhpVzukMMhjh9DkSktg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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x271d84fac18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "m = 200 # Measurements\n",
    "vx= 20 # in X\n",
    "vy= 10 # in Y\n",
    "acc = 5\n",
    "u_u  =  np.array(acc+np.random.randn(m))\n",
    "mx = np.array(vx+2*np.random.randn(m))\n",
    "my = np.array(vy+2*np.random.randn(m))\n",
    "u = np.vstack((u_u))\n",
    "print(u.shape, \"u\")\n",
    "\n",
    "measurements = np.vstack((mx))\n",
    "\n",
    "print(measurements.shape)\n",
    "\n",
    "print('Standard Deviation of Acceleration Measurements=%.2f' % np.std(mx))\n",
    "print('You assumed %.2f in R.' % R[0,0])\n",
    "\n",
    "\n",
    "fig = plt.figure(figsize=(16,5))\n",
    "\n",
    "plt.step(range(m),mx, label='$\\dot x$')\n",
    "#plt.step(range(m),my, label='$\\dot y$')\n",
    "plt.step(range(m),u_u, label='$u$')\n",
    "plt.ylabel(r'Velocity $m/s$')\n",
    "plt.title('Measurements')\n",
    "plt.legend(loc='best',prop={'size':18})\n",
    "plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 324,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200]\n"
     ]
    }
   ],
   "source": [
    "aer = []\n",
    "for i in range(len(measurements)):\n",
    "    i+=1\n",
    "    aer.append(i)\n",
    "print (aer)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Preallocation for Plotting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 325,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "xt = []\n",
    "#yt = []\n",
    "dxt= []\n",
    "#dyt= []\n",
    "Zx = []\n",
    "#Zy = []\n",
    "Px = []\n",
    "#Py = []\n",
    "Pdx= []\n",
    "#Pdy= []\n",
    "Rdx= []\n",
    "#Rdy= []\n",
    "Kx = []\n",
    "#Ky = []\n",
    "Kdx= []\n",
    "#Kdy= []\n",
    "\n",
    "def savestates(x, Z, P, R, K):\n",
    "    xt.append(float(x[0]))\n",
    "    #yt.append(float(x[1]))\n",
    "    dxt.append(float(x[1]))\n",
    "    #dyt.append(float(x[3]))\n",
    "    Zx.append(float(Z[0]))\n",
    "    #Zy.append(float(Z[1]))\n",
    "    Px.append(float(P[0,0]))\n",
    "    #Py.append(float(P[1,1]))\n",
    "    Pdx.append(float(P[1,1]))\n",
    "    #Pdy.append(float(P[3,3]))\n",
    "    Rdx.append(float(R[0,0]))\n",
    "    #Rdy.append(float(R[1,1]))\n",
    "    Kx.append(float(K[0,0]))\n",
    "    #Ky.append(float(K[1,0]))\n",
    "    Kdx.append(float(K[1,0]))\n",
    "    #Kdy.append(float(K[3,0]))  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Kalman Filter Algorithm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Filtering step Prediction / Predict\n",
    "This part of the Kalman filter now dares to predict the state of the system in the future. In addition, under certain conditions (observability) a state can be calculated with it which can not be measured! That's amazing, but in our case exactly what we need. We can not measure the position of the vehicle because the GPS of the navigation device has no reception in a tunnel. By initializing the state vector with a position and measuring the velocity, however, the dynamics still be used to make an optimal prediction about the position.A\n",
    "\n",
    "#### *xt+1=A⋅xt*\n",
    "\n",
    "The covariance must also be recalculated. Uncertainty about the state of the system increases in the Predict step, as we have seen in the 1D case. In the multidimensional case, the measurement uncertainty Q is additively added, so the uncertainty P is getting bigger and bigger.PQP\n",
    "\n",
    "#### *P=A⋅P⋅A‘+Q*\n",
    "\n",
    "That's it. We have in the future ( ) expected. The Kalman filter has made a statement about the expected system state in the future.dt\n",
    "\n",
    "Goes by now exactly time and the filter is in measuring / correcting and checking whether the prediction of the system state fits well with the new measurements. If so, the covariance chosen to be smaller by the filter (it is safer), if not, larger (something is wrong, the filter becomes more uncertain).dtP\n",
    "Filter step Measure / Correct\n",
    "The following mathematical calculations are not something that one must necessarily be able to derive. Rudolf E. Kalman thought about that in a few quiet minutes and it looks crazy, but works.\n",
    "\n",
    "From the sensors come current measured values , with which an innovation  the state vector  with the measuring matrix  calculated.\n",
    "\n",
    "#### *w=Z−(H⋅x)*\n",
    "Then it is looked at with which variance (which in the multi-dimensional case is called covariance matrix) can be further calculated. For this, the uncertainty and the measurement matrix and the measurement uncertainty required.PHR\n",
    "S=(H⋅P⋅H′+R)\n",
    "This determines the so-called Kalman gain. It states whether the readings or system dynamics should be more familiar.\n",
    "\n",
    "#### *K= P⋅ H'S*\n",
    "The Kalman Gain will decrease if the readings match the predicted system state. If the measured values ​​say otherwise, the elements of matrix K become larger.\n",
    "\n",
    "This information is now used to update the system state.\n",
    "\n",
    "#### *x = x + ( K⋅ w )*\n",
    "And also determined a new covariance for the upcoming Predict step.\n",
    "\n",
    "#### *P= ( I- ( K⋅ H) ) ⋅ P*\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 326,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 18.49712669])"
      ]
     },
     "execution_count": 326,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "measurements[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 327,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def kalman_filter(x,P):\n",
    "    for n in range(len(measurements)): \n",
    "        x = A*x + B*u[n]      \n",
    "        P = A*P*A.T        \n",
    "        S = H*P*H.T + R\n",
    "        K = (P*H.T) * np.linalg.pinv(S)       \n",
    "        Z = measurements[n]\n",
    "        y = Z - (H*x)                            \n",
    "        x = x + (K*y)        \n",
    "        P = (I - (K*H))*P        \n",
    "        savestates(x, Z, P, R, K)\n",
    "        print(\"x:\", x)\n",
    "        print(\"P:\", P)\n",
    "        print(\"K:\", K)\n",
    "        print(\"Z:\", Z)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### The Usual Step :\n",
    "1.  ##### Time Update (Prediction)\n",
    "2.  ##### Project the state ahead\n",
    "3.  ##### Project the error covariance ahead\n",
    "4.  ##### Measurement Update (Correction)\n",
    "5.  ##### Compute the Kalman Gain\n",
    "6.  ##### Update the estimate via z\n",
    "7.  ##### Update the error covariance\n",
    "8.  ##### Save states for Plotting\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 328,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x: [[ 8.70968852]\n",
      " [ 2.09771907]]\n",
      "P: [[ 50.02063368   0.41267367]\n",
      " [  0.41267367   8.25347334]]\n",
      "K: [[ 0.50020634  0.00412674]\n",
      " [ 0.00412674  0.08253473]]\n",
      "Z: [ 16.93424067]\n",
      "x: [[ 12.31423379]\n",
      " [  3.61760869]]\n",
      "P: [[ 33.40948835   0.76155018]\n",
      " [  0.76155018   7.61550178]]\n",
      "K: [[ 0.33409488  0.0076155 ]\n",
      " [ 0.0076155   0.07615502]]\n",
      "Z: [ 18.49712669]\n",
      "x: [[ 16.17296086]\n",
      " [  5.79215294]]\n",
      "P: [[ 25.15888584   1.05923892]\n",
      " [  1.05923892   7.06159278]]\n",
      "K: [[ 0.25158886  0.01059239]\n",
      " [ 0.01059239  0.07061593]]\n",
      "Z: [ 24.82515966]\n",
      "x: [[ 18.08968898]\n",
      " [  7.38985687]]\n",
      "P: [[ 20.26296567   1.31482834]\n",
      " [  1.31482834   6.57414171]]\n",
      "K: [[ 0.20262966  0.01314828]\n",
      " [ 0.01314828  0.06574142]]\n",
      "Z: [ 21.28166656]\n",
      "x: [[ 19.79223812]\n",
      " [  8.92053103]]\n",
      "P: [[ 17.05042925   1.53505032]\n",
      " [  1.53505032   6.14020126]]\n",
      "K: [[ 0.17050429  0.0153505 ]\n",
      " [ 0.0153505   0.06140201]]\n",
      "Z: [ 21.65750423]\n",
      "x: [[ 20.97825195]\n",
      " [  9.97964675]]\n",
      "P: [[ 14.80322004   1.72501917]\n",
      " [  1.72501917   5.75006389]]\n",
      "K: [[ 0.1480322   0.01725019]\n",
      " [ 0.01725019  0.05750064]]\n",
      "Z: [ 20.10751177]\n",
      "x: [[ 22.19085507]\n",
      " [ 10.82865836]]\n",
      "P: [[ 13.16105049   1.88871567]\n",
      " [  1.88871567   5.3963305 ]]\n",
      "K: [[ 0.1316105   0.01888716]\n",
      " [ 0.01888716  0.0539633 ]]\n",
      "Z: [ 21.11870043]\n",
      "x: [[ 23.35134937]\n",
      " [ 11.77810279]]\n",
      "P: [[ 11.92283603   2.02931229]\n",
      " [  2.02931229   5.07328072]]\n",
      "K: [[ 0.11922836  0.02029312]\n",
      " [ 0.02029312  0.05073281]]\n",
      "Z: [ 20.32984239]\n",
      "x: [[ 24.88909208]\n",
      " [ 12.86477127]]\n",
      "P: [[ 10.96722834   2.14939631]\n",
      " [  2.14939631   4.77643625]]\n",
      "K: [[ 0.10967228  0.02149396]\n",
      " [ 0.02149396  0.04776436]]\n",
      "Z: [ 23.23847578]\n",
      "x: [[ 25.84038711]\n",
      " [ 13.56461264]]\n",
      "P: [[ 10.21647187   2.25112556]\n",
      " [  2.25112556   4.50225113]]\n",
      "K: [[ 0.10216472  0.02251126]\n",
      " [ 0.02251126  0.04502251]]\n",
      "Z: [ 18.95120644]\n",
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      "Z: [ 19.21750929]\n",
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      "K: [[ 0.0842224   0.02507962]\n",
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      "Z: [ 16.54950503]\n",
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      " [ 15.776736  ]]\n",
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      " [ 2.54141566  3.38855422]]\n",
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      " [ 0.02564833  0.03206042]]\n",
      "Z: [ 21.67926195]\n",
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      " [ 2.57918781  3.0343386 ]]\n",
      "K: [[ 0.07747865  0.02579188]\n",
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      "Z: [ 21.099611]\n",
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      "Z: [ 21.59469609]\n",
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      "Z: [ 14.6849106]\n",
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      " [ 17.853444  ]]\n",
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      " [ 0.0160177   0.00696422]]\n",
      "Z: [ 20.81838213]\n",
      "x: [[ 49.00837386]\n",
      " [ 18.04664996]]\n",
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      "Z: [ 22.03746727]\n",
      "x: [[ 49.10977701]\n",
      " [ 17.87643208]]\n",
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      "Z: [ 18.26953944]\n",
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      " [ 0.01422665  0.00557908]]\n",
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      " [ 0.18106468  0.02045929]]\n",
      "K: [[ 0.0216422   0.00181065]\n",
      " [ 0.00181065  0.00020459]]\n",
      "Z: [ 20.46731909]\n",
      "x: [[ 162.10627889]\n",
      " [  44.25109745]]\n",
      "P: [[ 2.15293148  0.17913171]\n",
      " [ 0.17913171  0.02012716]]\n",
      "K: [[ 0.02152931  0.00179132]\n",
      " [ 0.00179132  0.00020127]]\n",
      "Z: [ 18.37649018]\n",
      "x: [[ 163.63026472]\n",
      " [  44.43614463]]\n",
      "P: [[ 2.14175589  0.17722909]\n",
      " [ 0.17722909  0.01980213]]\n",
      "K: [[ 0.02141756  0.00177229]\n",
      " [ 0.00177229  0.00019802]]\n",
      "Z: [ 22.73529677]\n",
      "x: [[ 165.14376931]\n",
      " [  44.653548  ]]\n",
      "P: [[ 2.1306918   0.17535618]\n",
      " [ 0.17535618  0.01948402]]\n",
      "K: [[ 0.02130692  0.00175356]\n",
      " [ 0.00175356  0.00019484]]\n",
      "Z: [ 21.47239168]\n",
      "x: [[ 166.65115134]\n",
      " [  44.97021511]]\n",
      "P: [[ 2.1197376   0.17351238]\n",
      " [ 0.17351238  0.01917264]]\n",
      "K: [[ 0.02119738  0.00173512]\n",
      " [ 0.00173512  0.00019173]]\n",
      "Z: [ 18.74945733]\n",
      "x: [[ 168.16508442]\n",
      " [  45.14546032]]\n",
      "P: [[ 2.10889175  0.17169711]\n",
      " [ 0.17169711  0.01886781]]\n",
      "K: [[ 0.02108892  0.00171697]\n",
      " [ 0.00171697  0.00018868]]\n",
      "Z: [ 21.49771197]\n",
      "x: [[ 169.69603843]\n",
      " [  45.40627985]]\n",
      "P: [[ 2.09815269  0.16990977]\n",
      " [ 0.16990977  0.01856937]]\n",
      "K: [[ 0.02098153  0.0016991 ]\n",
      " [ 0.0016991   0.00018569]]\n",
      "Z: [ 20.28787715]\n",
      "x: [[ 171.27764849]\n",
      " [  45.72878918]]\n",
      "P: [[ 2.08751892  0.16814982]\n",
      " [ 0.16814982  0.01827715]]\n",
      "K: [[ 0.02087519  0.0016815 ]\n",
      " [ 0.0016815   0.00018277]]\n",
      "Z: [ 20.7847191]\n",
      "x: [[ 172.82886898]\n",
      " [  45.99846915]]\n",
      "P: [[ 2.07698896  0.16641671]\n",
      " [ 0.16641671  0.017991  ]]\n",
      "K: [[ 0.02076989  0.00166417]\n",
      " [ 0.00166417  0.00017991]]\n",
      "Z: [ 19.88335327]\n",
      "x: [[ 174.30910821]\n",
      " [  46.14130412]]\n",
      "P: [[ 2.06656136  0.16470989]\n",
      " [ 0.16470989  0.01771074]]\n",
      "K: [[ 0.02066561  0.0016471 ]\n",
      " [ 0.0016471   0.00017711]]\n",
      "Z: [ 18.96735755]\n",
      "x: [[ 175.89218295]\n",
      " [  46.41508534]]\n",
      "P: [[ 2.05623467  0.16302885]\n",
      " [ 0.16302885  0.01743624]]\n",
      "K: [[ 0.02056235  0.00163029]\n",
      " [ 0.00163029  0.00017436]]\n",
      "Z: [ 20.78943893]\n",
      "x: [[ 177.40621787]\n",
      " [  46.69743594]]\n",
      "P: [[ 2.04600751  0.16137308]\n",
      " [ 0.16137308  0.01716735]]\n",
      "K: [[ 0.02046008  0.00161373]\n",
      " [ 0.00161373  0.00017167]]\n",
      "Z: [ 16.83595474]\n",
      "x: [[ 178.89586833]\n",
      " [  46.83060858]]\n",
      "P: [[ 2.03587848  0.15974208]\n",
      " [ 0.15974208  0.01690392]]\n",
      "K: [[ 0.02035878  0.00159742]\n",
      " [ 0.00159742  0.00016904]]\n",
      "Z: [ 18.50243643]\n",
      "x: [[ 180.44776921]\n",
      " [  47.02894204]]\n",
      "P: [[ 2.02584624  0.15813537]\n",
      " [ 0.15813537  0.01664583]]\n",
      "K: [[ 0.02025846  0.00158135]\n",
      " [ 0.00158135  0.00016646]]\n",
      "Z: [ 19.97982768]\n",
      "x: [[ 182.12796087]\n",
      " [  47.3622487 ]]\n",
      "P: [[ 2.01590944  0.15655247]\n",
      " [ 0.15655247  0.01639293]]\n",
      "K: [[ 0.02015909  0.00156552]\n",
      " [ 0.00156552  0.00016393]]\n",
      "Z: [ 22.75034654]\n",
      "x: [[ 183.68719184]\n",
      " [  47.5341625 ]]\n",
      "P: [[ 2.00606679  0.15499292]\n",
      " [ 0.15499292  0.0161451 ]]\n",
      "K: [[ 0.02006067  0.00154993]\n",
      " [ 0.00154993  0.00016145]]\n",
      "Z: [ 20.0087091]\n",
      "x: [[ 185.29982385]\n",
      " [  47.80742592]]\n",
      "P: [[ 1.996317    0.15345628]\n",
      " [ 0.15345628  0.0159022 ]]\n",
      "K: [[ 0.01996317  0.00153456]\n",
      " [ 0.00153456  0.00015902]]\n",
      "Z: [ 20.09415291]\n",
      "x: [[ 186.93476537]\n",
      " [  48.1342959 ]]\n",
      "P: [[ 1.9866588   0.15194209]\n",
      " [ 0.15194209  0.01566413]]\n",
      "K: [[ 0.01986659  0.00151942]\n",
      " [ 0.00151942  0.00015664]]\n",
      "Z: [ 19.36958681]\n",
      "x: [[ 188.60516745]\n",
      " [  48.36586718]]\n",
      "P: [[ 1.97709095  0.15044994]\n",
      " [ 0.15044994  0.01543076]]\n",
      "K: [[ 0.01977091  0.0015045 ]\n",
      " [ 0.0015045   0.00015431]]\n",
      "Z: [ 22.59847884]\n",
      "x: [[ 190.12997873]\n",
      " [  48.56514535]]\n",
      "P: [[ 1.96761223  0.14897939]\n",
      " [ 0.14897939  0.01520198]]\n",
      "K: [[ 0.01967612  0.00148979]\n",
      " [ 0.00148979  0.00015202]]\n",
      "Z: [ 15.93300447]\n",
      "x: [[ 191.75329791]\n",
      " [  48.81388631]]\n",
      "P: [[ 1.95822145  0.14753004]\n",
      " [ 0.14753004  0.01497767]]\n",
      "K: [[ 0.01958221  0.0014753 ]\n",
      " [ 0.0014753   0.00014978]]\n",
      "Z: [ 19.28531266]\n",
      "x: [[ 193.41676852]\n",
      " [  49.12266493]]\n",
      "P: [[ 1.94891742  0.1461015 ]\n",
      " [ 0.1461015   0.01475773]]\n",
      "K: [[ 0.01948917  0.00146102]\n",
      " [ 0.00146102  0.00014758]]\n",
      "Z: [ 19.36763106]\n",
      "x: [[ 194.9989704 ]\n",
      " [  49.22971159]]\n",
      "P: [[ 1.93969898  0.14469336]\n",
      " [ 0.14469336  0.01454205]]\n",
      "K: [[ 0.01939699  0.00144693]\n",
      " [ 0.00144693  0.00014542]]\n",
      "Z: [ 19.52272572]\n",
      "x: [[ 196.7901803]\n",
      " [  49.6566246]]\n",
      "P: [[ 1.930565    0.14330526]\n",
      " [ 0.14330526  0.01433053]]\n",
      "K: [[ 0.01930565  0.00143305]\n",
      " [ 0.00143305  0.00014331]]\n",
      "Z: [ 22.32952567]\n"
     ]
    }
   ],
   "source": [
    "kalman_filter(x,P)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### State Estimate $x$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 329,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
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       "       [ 20.28476409],\n",
       "       [ 19.90901643],\n",
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       "       [ 18.30396186],\n",
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       "       [ 20.31562863],\n",
       "       [ 19.22021087],\n",
       "       [ 21.94502102],\n",
       "       [ 22.44752271],\n",
       "       [ 18.3435276 ],\n",
       "       [ 17.73713316],\n",
       "       [ 18.47844804],\n",
       "       [ 21.60265158],\n",
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       "       [ 17.60187598],\n",
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       "       [ 19.90984421],\n",
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       "       [ 19.52825711],\n",
       "       [ 20.9105609 ],\n",
       "       [ 21.37267281],\n",
       "       [ 20.84638764],\n",
       "       [ 21.93546231],\n",
       "       [ 17.492414  ],\n",
       "       [ 21.5640507 ],\n",
       "       [ 19.75569178],\n",
       "       [ 18.67322951],\n",
       "       [ 19.01828879],\n",
       "       [ 21.77062757],\n",
       "       [ 17.85411938],\n",
       "       [ 20.37605513],\n",
       "       [ 21.75575635],\n",
       "       [ 21.15021673],\n",
       "       [ 24.62149955],\n",
       "       [ 23.72609143],\n",
       "       [ 19.08123669],\n",
       "       [ 18.44810829],\n",
       "       [ 17.2252362 ],\n",
       "       [ 21.06529376],\n",
       "       [ 20.95639275],\n",
       "       [ 21.55903391],\n",
       "       [ 18.96661409],\n",
       "       [ 15.08931285],\n",
       "       [ 16.99715445],\n",
       "       [ 19.5287363 ],\n",
       "       [ 18.04328272],\n",
       "       [ 18.48303552],\n",
       "       [ 21.41632279],\n",
       "       [ 21.42446675],\n",
       "       [ 20.46731909],\n",
       "       [ 18.37649018],\n",
       "       [ 22.73529677],\n",
       "       [ 21.47239168],\n",
       "       [ 18.74945733],\n",
       "       [ 21.49771197],\n",
       "       [ 20.28787715],\n",
       "       [ 20.7847191 ],\n",
       "       [ 19.88335327],\n",
       "       [ 18.96735755],\n",
       "       [ 20.78943893],\n",
       "       [ 16.83595474],\n",
       "       [ 18.50243643],\n",
       "       [ 19.97982768],\n",
       "       [ 22.75034654],\n",
       "       [ 20.0087091 ],\n",
       "       [ 20.09415291],\n",
       "       [ 19.36958681],\n",
       "       [ 22.59847884],\n",
       "       [ 15.93300447],\n",
       "       [ 19.28531266],\n",
       "       [ 19.36763106],\n",
       "       [ 19.52272572],\n",
       "       [ 22.32952567]])"
      ]
     },
     "execution_count": 329,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "measurements"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 330,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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kySoAAHMy/RcYJMkqAADzMv0XGBTJKgAAAM3RrAIAANAcy4ABAEhioBLQFskq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\nAOiOWAUAAKA7YhUAAIDu/D9TjFq8/Kb9OQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x271d862add8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_x():\n",
    "    fig = plt.figure(figsize=(16,16))\n",
    "    plt.step(range(200),dxt, label='$\\dot x$')\n",
    "    #plt.step(range(200)),dyt, label='$\\dot y$')\n",
    "\n",
    "    plt.axhline(vx, color='#999999', label='$\\dot x_{real}$')\n",
    "    #plt.axhline(vy, color='#999999', label='$\\dot y_{real}$')\n",
    "\n",
    "    plt.xlabel('Filter Step')\n",
    "    plt.title('Estimate (Elements from State Vector $x$)')\n",
    "    plt.legend(loc='best',prop={'size':22})\n",
    "    plt.ylim([0, 50])\n",
    "    plt.ylabel('Velocity')\n",
    "\n",
    "\n",
    "\n",
    "plot_x()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 331,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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JdW1e52RJkiRJ2ugYQJspKkyF9RoXIpIkSZKknDKANtN4D2itAVSSJEmScskA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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x271d9657da0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_K():\n",
    "    fig = plt.figure(figsize=(16,9))\n",
    "    plt.plot(range(200),Kx, label='Kalman Gain for $x$')\n",
    "    #plt.plot(range(len(measurements[0])),Ky, label='Kalman Gain for $y$')\n",
    "    plt.plot(range(200),Kdx, label='Kalman Gain for $\\dot x$')\n",
    "   # plt.plot(range(len(measurements[0])),Kdy, label='Kalman Gain for $\\dot y$')\n",
    "\n",
    "    plt.xlabel('Filter Step')\n",
    "    plt.ylabel('')\n",
    "    plt.title('Kalman Gain (the lower, the more the measurement fullfill the prediction)')\n",
    "    plt.legend(loc='best',prop={'size':22})\n",
    "\n",
    "\n",
    "\n",
    "plot_K()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 332,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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AAJar973vspx//nl5wxt++0eeq9Vqueiit+T888/Lm970uxkdHT2ktQmddR3V9ozavRYA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\nmn+7/bM5ffiUnDR4QrPLWhK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fZ57wtJyz+iy73QKHTLW9LSv6u7Ki/8C7+U41Ojae7fVg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\nlvktwqZQAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x271d8998208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_P():\n",
    "    fig = plt.figure(figsize=(16,9))\n",
    "    plt.plot(range(200),Px, label='$x$')\n",
    "    #plt.plot(range(len(measurements[0])),Py, label='$y$')\n",
    "    plt.plot(range(200),Pdx, label='$\\dot x$')\n",
    "    #plt.plot(range(len(measurements[0])),Pdy, label='$\\dot y$')\n",
    "\n",
    "    plt.xlabel('Filter Step')\n",
    "    plt.ylabel('')\n",
    "    plt.title('Uncertainty (Elements from Matrix $P$)')\n",
    "    plt.legend(loc='best',prop={'size':22})\n",
    "\n",
    "\n",
    "plot_P()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 333,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n"
     ]
    }
   ],
   "source": [
    "print(len(measurements[0]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 334,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[8.253473336695858,\n",
       " 7.615501776950413,\n",
       " 7.061592781482934,\n",
       " 6.574141709276844,\n",
       " 6.140201262152482,\n",
       " 5.750063889598774,\n",
       " 5.396330495263222,\n",
       " 5.073280721533259,\n",
       " 4.776436247843971,\n",
       " 4.502251125562782,\n",
       " 4.247887855760608,\n",
       " 4.011052678491844,\n",
       " 3.789872618170334,\n",
       " 3.582802547770701,\n",
       " 3.3885542168674703,\n",
       " 3.2060416072955262,\n",
       " 3.0343385984727167,\n",
       " 2.8726460261729976,\n",
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       " 2.441042053730048,\n",
       " 2.3131489667934617,\n",
       " 2.192448233861145,\n",
       " 2.07852193995381,\n",
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       " 1.8694694861036096,\n",
       " 1.7736436552825015,\n",
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       " 0.1031341316679079,\n",
       " 0.10036471421983979,\n",
       " 0.09769144266380665,\n",
       " 0.09511027508005096,\n",
       " 0.09261736678535393,\n",
       " 0.09020905949538037,\n",
       " 0.08788187114174158,\n",
       " 0.08563248630118071,\n",
       " 0.0834577471972105,\n",
       " 0.08135464523725033,\n",
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       " 0.07181786988197915,\n",
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       " 0.0684139071790512,\n",
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       " 0.06521833649763024,\n",
       " 0.06369381674581198,\n",
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       " 0.06078228831132943,\n",
       " 0.05939190607104049,\n",
       " 0.058042984054302284,\n",
       " 0.05673401204021796,\n",
       " 0.0554635442745444,\n",
       " 0.054230196337412905,\n",
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       " 0.05073988620171063,\n",
       " 0.049642299651952174,\n",
       " 0.04857573253553975,\n",
       " 0.04753911148344198,\n",
       " 0.04653140676075475,\n",
       " 0.0455516302422333,\n",
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       " 0.043672105946587894,\n",
       " 0.042770573180331756,\n",
       " 0.0418933952734939,\n",
       " 0.04103976525254261,\n",
       " 0.04020890761333313,\n",
       " 0.03940007691770558,\n",
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       " 0.0378456570006054,\n",
       " 0.0370987155600256,\n",
       " 0.036371094274886544,\n",
       " 0.035662179307852454,\n",
       " 0.03497137981133318,\n",
       " 0.0342981269411786,\n",
       " 0.03364187291782494,\n",
       " 0.03300209013237494,\n",
       " 0.03237827029523935,\n",
       " 0.031769923625103495,\n",
       " 0.03117657807611058,\n",
       " 0.030597778601273443,\n",
       " 0.030033086450239242,\n",
       " 0.029482078499637267,\n",
       " 0.028944346614339474,\n",
       " 0.028419497038056764,\n",
       " 0.02790714981178168,\n",
       " 0.027406938218670726,\n",
       " 0.026918508254037042,\n",
       " 0.026441518119197087,\n",
       " 0.025975637737983642,\n",
       " 0.025520548294801933,\n",
       " 0.025075941793166568,\n",
       " 0.024641520633714102,\n",
       " 0.02421699721073998,\n",
       " 0.0238020935263594,\n",
       " 0.023396540821439455,\n",
       " 0.023000079222495005,\n",
       " 0.02261245740378327,\n",
       " 0.022233432263872206,\n",
       " 0.021862768615995554,\n",
       " 0.021500238891543143,\n",
       " 0.0211456228560687,\n",
       " 0.020798707337229223,\n",
       " 0.0204592859641,\n",
       " 0.020127158917337667,\n",
       " 0.019802132689690586,\n",
       " 0.01948401985638103,\n",
       " 0.019172638854907664,\n",
       " 0.018867813773839396,\n",
       " 0.01856937415019314,\n",
       " 0.018277154775008138,\n",
       " 0.017990995506748788,\n",
       " 0.0177107410921859,\n",
       " 0.017436240994423615,\n",
       " 0.017167349227755327,\n",
       " 0.016903924199047383,\n",
       " 0.016645828555363947,\n",
       " 0.01639292903756013,\n",
       " 0.016145096339583682,\n",
       " 0.015902204973237837,\n",
       " 0.01566413313816976,\n",
       " 0.015430762596860107,\n",
       " 0.015201978554399868,\n",
       " 0.014977669542850664,\n",
       " 0.014757727309994187,\n",
       " 0.014542046712285532,\n",
       " 0.014330525611833756]"
      ]
     },
     "execution_count": 334,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Pdx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 335,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(200, 1)\n"
     ]
    }
   ],
   "source": [
    "print(measurements.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 336,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
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+IUly3XU1q1cfka9//bp88pNX5/Wv//O88pV/mD177pnX3wUAAJivfXODOqtW750bdNZp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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x271d90229e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_xy():\n",
    "    fig = plt.figure(figsize=(16,16))\n",
    "    \n",
    "   \n",
    "    plt.scatter(aer,xt, s=20, label='State', c='k')\n",
    "    #plt.scatter(rr,i, s=5, label='original', c='b')\n",
    "    plt.scatter(aer[0],xt[0], s=100, label='Start', c='g')\n",
    "    plt.scatter(aer[-1],xt[-1], s=100, label='Goal', c='r')\n",
    "\n",
    "    plt.xlabel('X')\n",
    "    plt.ylabel('Time Step')\n",
    "    plt.title('Position')\n",
    "    plt.legend(loc='best')\n",
    "    plt.axis('equal')\n",
    "    \n",
    "plot_xy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 337,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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GTjvtzPzBH/xRBgYeHvd3jpWVWAAAgAZteNVrMvfzF424pXhg7rz0ve514/7s+fPn56yz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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x271d891cbe0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_dxt():\n",
    "    fig = plt.figure(figsize=(16,16))\n",
    "    \n",
    "   \n",
    "    plt.scatter(aer,dxt,s=20, label='State', c='k')\n",
    "    #plt.scatter(vx_o[0],vx_o[1], s=5, label='original', c='b')\n",
    "    plt.scatter(aer[0], dxt[0],s=100, label='Start', c='g')\n",
    "    plt.scatter(aer[-1], dxt[-1], s=100, label='Goal', c='r')\n",
    "    \n",
    "    \"\"\"\"\"\n",
    "    plt.scatter(aer,measurements,s=10, label='State', c='y')\n",
    "    #plt.scatter(vx_o[0],vx_o[1], s=5, label='original', c='b')\n",
    "    plt.scatter(aer[0], measurements[0],s=100, label='Start', c='g')\n",
    "    plt.scatter(aer[-1], measurements[-1], s=100, label='Goal', c='r')\n",
    "    \"\"\"\"\"\n",
    "    plt.xlabel('Velocity at X')\n",
    "    plt.ylabel('Time Step')\n",
    "    plt.title('Velocity')\n",
    "    plt.legend(loc='best')\n",
    "    plt.axis('equal')\n",
    "    \n",
    "plot_dxt()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "vx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "dxt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "vy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "dyt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "u = []\n",
    "for i in range(0,200):\n",
    "    u.append(i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "u"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Kalman Filter - Udacity Assignment"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "xt = []\n",
    "yt = []\n",
    "dxt= []\n",
    "dyt= []\n",
    "Zx = []\n",
    "Zy = []\n",
    "Px = []\n",
    "Py = []\n",
    "Pdx= []\n",
    "Pdy= []\n",
    "Rdx= []\n",
    "Rdy= []\n",
    "Kx = []\n",
    "Ky = []\n",
    "Kdx= []\n",
    "Kdy= []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def filter(x, P):\n",
    "    plt.scatter([x[0]], [x[1]], s=100)\n",
    "    plt.title('Initial Location')\n",
    "\n",
    "    for n in range(len(measurements)):\n",
    "\n",
    "        # prediction\n",
    "        x = (F * x) + u\n",
    "        P = (F * P * F.transpose()) + Q\n",
    "        \n",
    "\n",
    "        # measurement update\n",
    "        Z = np.matrix(measurements[n])\n",
    "        \n",
    "        y = Z.transpose() - (H * x)\n",
    "       \n",
    "        S = H * P * H.transpose() + R\n",
    "        K = P * H.transpose() * inv(S)\n",
    "        x = x + (K * y)\n",
    "        P = (I - (K * H)) * P\n",
    "               \n",
    "        xt.append(float(x[0]))\n",
    "        yt.append(float(x[1]))\n",
    "        dxt.append(float(x[2]))\n",
    "        dyt.append(float(x[3]))\n",
    "        #Zx.append(float(Z[0]))\n",
    "        #Zy.append(float(Z[1]))\n",
    "        Px.append(float(P[0,0]))\n",
    "        Py.append(float(P[1,1]))\n",
    "        Pdx.append(float(P[2,2]))\n",
    "        Pdy.append(float(P[3,3]))\n",
    "        Rdx.append(float(R[0,0]))\n",
    "        Rdy.append(float(R[1,1]))\n",
    "        Kx.append(float(K[0,0]))\n",
    "        Ky.append(float(K[1,0]))\n",
    "        Kdx.append(float(K[2,0]))\n",
    "        Kdy.append(float(K[3,0]))\n",
    "        #print('X:',x)\n",
    "        #print(P)\n",
    "\n",
    "\n",
    "dt = 0.1\n",
    "u = np.matrix([[0.], [0.], [0.], [0.]])\n",
    "measurements = np.matrix([[5.0, 10.0], [6.0, 8.0], [7.0, 6.0], [8.0, 4.0], [9.0, 2.0], [10.0, 0.0]])\n",
    "#measurements = np.matrix([[1., 4.], [6., 0.], [11., -4.], [16., -8.]])\n",
    "#measurements = np.matrix([[1., 17.], [1., 15.], [1., 13.], [1., 11.]])\n",
    "o = [[5.0, 10.0], [6.0, 8.0], [7.0, 6.0], [8.0, 4.0], [9.0, 2.0], [10.0, 0.0]]\n",
    "\n",
    "x = np.matrix([[4.], [12.], [0.0], [0.0]])# initial state (location and velocity)\n",
    "#x = np.matrix([[-4.], [8.], [0.0], [0.0]])\n",
    "#x = np.matrix([[1.], [19.], [0.0], [0.0]])\n",
    "\n",
    "P = np.matrix([[0.0, 0.0, 0.0, 0.0],\n",
    "              [0.0, 0.0, 0.0, 0.0],\n",
    "              [0.0, 0.0, 1000, 0.0],\n",
    "              [0.0, 0.0, 0.0, 1000]]) # initial uncertainty: 0 for positions x and y, 1000 for the two velocities\n",
    "\n",
    "F = np.matrix([[1.0, 0.0, dt, 0.0],\n",
    "              [0.0, 1.0, 0.0, dt],\n",
    "              [0.0, 0.0, 1.0, 0.0],\n",
    "              [0.0, 0.0, 0.0, 1.0]]) # next state function: generalize the 2d version to 4d\n",
    "\n",
    "\n",
    "H = np.matrix([[1.0, 0.0, 0.0, 0.0], [0.0, 1.0, 0.0, 0.0]]) # measurement function: reflect the fact that we observe x and y but not the two velocities\n",
    "\n",
    "R = np.matrix([[1.0, 0.0], [0.0, 1.0]]) # measurement uncertainty: use 2x2 matrix with 0.1 as main diagonal\n",
    "\n",
    "I = np.matrix([[1.0, 0.0, 0.0, 0.0], [0.0, 1.0, 0.0, 0.0], [0.0, 0.0, 1.0, 0.0], [0.0, 0.0, 0.0, 1.0]]) # 4d identity matrix\n",
    "\n",
    "sv = 1.0\n",
    "\n",
    "G = np.matrix([[dt**2],\n",
    "               [dt**2],\n",
    "               [dt],\n",
    "               [dt]])\n",
    "\n",
    "\n",
    "Q = G*G.T*sv**2\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "filter(x,P)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "fig = plt.figure(figsize=(16,16))\n",
    "plt.scatter(xt,yt, s=20, label='State', c='k')\n",
    "plt.scatter(xt[0],yt[0], s=100, label='Start', c='g')\n",
    "plt.scatter(xt[-1],yt[-1], s=200, label='Goal', c='r')\n",
    "plt.scatter(o[0][0],o[0][1], s=100, label='Start-measurement', c='y')\n",
    "plt.scatter(o[-1][0] ,o[-1][1], s=100, label='Goal-measurement', c='y')\n",
    "for i in range (len(o)):\n",
    "    plt.scatter(o[i][0],o[i][1], s=20, label='State', c='b')\n",
    "\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('Y')\n",
    "plt.title('Position')\n",
    "plt.legend(loc='best')\n",
    "plt.axis('equal')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "int(5.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "measurements"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "xt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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